Jim Hoste

Biography

Education and Employment

I received my A.B and M.A. in Mathematics from the University of California, Berkeley in 1976 and 1978 respectively. In 1982 I earned my Ph.D. in Mathematics from the University of Utah under the supervision of Ronald J. Stern. After receiving my doctorate I was awarded a National Science Foundation Postdoctoral Fellowship which allowed me to visit the Courant Institute of Mathematical Sciences at New York University. Subsequently I held positions at Rutgers University, Oregon State University, and Pomona College before coming to Pitzer in 1989. I have spent time visiting the University of Melbourne, Australia, the University of Hawaii, Manoa, and the Mathematical Sciences Research Institute, Berkeley, California. I retired from Pitzer College in 2018.

Research

My research interests are primarily in knot theory and low-dimensional topology. While working at Rutgers, I had the good fortune to hear Vaughan Jones speak about a "New Polynomial Invariant of Knots" at the Institute for Advanced Study in Princeton. Within a few months I was one of several people that found the 2-variable generalization of the Jones polynomial, now knows as the Homfly polynomial. Following this, I wrote several papers with Jozef Przytycki about skein modules of 3-manifolds and worked on other problems that arise from the study of the skein polynomials of knots.

Over the years I have collaborated on the tabulation of all prime alternating knots through 18 crossings and prime nonalternating knots through 16 crossings. (This began as a project with six high school students at Claremont High School.) Together with Morwen Thistlethwaite, we have written a program called Knotscape that allows ready access to the knot tables as well as the computation of various knot invariants such as skein polynomials, representations of the fundamental group of a knot into permutation groups, and a number of hyperbolic invariants.

I am also interested in hyperbolic knots and various geometric knot invariants such as the A-polynomial. Most recently I have focussed on other invariants of knots, especially ones related to representations of the knot group, and also knot quandles.

Here is a list of my publications.

Claremont REU

During the three summers of 2005, 2006, and 2007, I was director of the Claremont Colleges Mathematics REU and directed undergraduate students in summer research projects.

Students

While on the faculty at Oregon State University, I supervised Helmut Doll's master's thesis, Tabulating Oriented Links.

I supervised the following students' Senior Thesis in Mathematics while in Claremont.

  1. Charlie McIntosh, Pitzer College, 2003.
  2. Rob Gaebler, Harvey Mudd College, 2004.
  3. Jessica May, Harvey Mudd College, 2006.
  4. Mayra Ibarra, Scripps College, 2010.
  5. Kristine Stanton, Pitzer College, 2011.
  6. Scott M. Garrabrant, Pitzer College, 2011.

Editorial Positions

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